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Founder  Joined: 18 Apr 2015
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The 500 students in a class took an examination. Sco [#permalink]
Expert's post 00:00

Question Stats: 26% (01:32) correct 73% (01:53) wrong based on 38 sessions

The 500 students in a class took an examination. Scores were given on an inte­ger scale of 0-100. Jamal's score was 2 standard deviations above the mean score on the examination, and Charlie's score was at exactly the 5th percentile. The distribution of exam scores was approximately normal. Which of the fol­lowing statements must be true?

Indicate all such statements.

❑ Jamal scored closer to the mean than Charlie.

❑ More than 400 students achieved scores less than or equal to Jamal's score and greater than or equal to Charlie's score.

❑ Fewer than 450 students achieved scores less than or equal to Jamal's score and greater than or equal to Charlie's score.

❑ At least one other person received the same score as Charlie.
[Reveal] Spoiler: OA

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Re: The 500 students in a class took an examination. Sco [#permalink]
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A:
You need to know that in a normal curve, the mean is exactly at the 50%ile, 1 standard deviation above the mean is 34%ile above that, and 2 standard deviations above the mean is 14%ile above that. In other words, 2 standard deviations above the mean is around 98%ile. Since Jamal is therefore at 98%ile and Charlie as at 5%ile, Charlie is closer to the mean and this answer is out.

B:
If Charlie is 5%ile, then he performed better than 5% of the total, or 25 people. Since Jamal is 98%ile, he performed better than 98% of the students, meaning about 2% of them, about 10 students, performed better than him. Since only about 35 people out of 500 performed either better or worse than them, 465 must have performed equal to Charlie or above or equal to Jamal or below, so we can see that this answer must be true.

C:
From the last answer choice, we know that we're looking at 465 people, which is well above 450, so this one is out.

D:
Since there are 500 students, every percentile must contain 5 students. The key to this one is the word "exactly". Since the 5th percentile falls between the 25th and 26th student, the 5th percentile itself is the average of the 25th and 26th students' scores. Since the scores are given in integers, if you average two of them, you'll either get an integer, or something that ends in a .5. But since Charlie couldn't have gotten a score that ends in a .5, this scenario is out.

What if the 25th lowest student had scored a 20 and the 26th lowest had gotten a 22? Then the 5th percentile would be 21, but since nobody actually got that score, this scenario is impossible.

The only way Charlie could've gotten exactly the 5th percentile is if the 25th and 26th lowest people got the same score, in which case the average of the two of them equals both of them. Thus, D is in.
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Founder  Joined: 18 Apr 2015
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Re: The 500 students in a class took an examination. Sco [#permalink]
Expert's post
Amazin explanation. As usual.

I missed it.
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Re: The 500 students in a class took an examination. Sco [#permalink]
Carcass wrote:
Amazin explanation. As usual.

I missed it.

Hello Carcass. Charlie score is at 5th percentile, which means p5. To find p5, we have to follow those steps:

1: position of p5 is L = 5 * (501)/100 = 25.05
2: M = 25
3: P5 = X25 + (25.05-25)(26-25) = 25.05

I don't understand exactly how D is resolved! I just did the previous logic while i was trying to approach for a solution. GRE Prep Club Legend  Joined: 07 Jun 2014
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Re: The 500 students in a class took an examination. Sco [#permalink]
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Expert's post
Avraheem wrote:

Hello Carcass. Charlie score is at 5th percentile, which means p5. To find p5, we have to follow those steps:

1: position of p5 is L = 5 * (501)/100 = 25.05
2: M = 25
3: P5 = X25 + (25.05-25)(26-25) = 25.05

I don't understand exactly how D is resolved! I just did the previous logic while i was trying to approach for a solution.

Hi,

Could you please clarify what you mena by X25 and M.

Percentile score is that score which divides the highest value in the previous bracket and the lowest value in the next %tile bracket. For example 1% means the score of the 5th and 6th student averaged.

So suppose we have the following score card

Student Rank:
1...2...3...4...5...6...7...8...9...10...11...12

Score:
12..14..14..15..15..16..17..17..17..18..18..19

1%ile score in the case above is 15.5. No one gets exactly one percentile. However 2%tile score is 18. Student number 10 and 11 both have that score.

In order to get an integer percentile you must have the last member of previous bracket and the first member of current bracket with thw same score.

Hence atleast one other guy must have scored the same points as charlie has an integer value of percentile.
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Re: The 500 students in a class took an examination. Sco [#permalink]
Hello Sandy

I am rusty on this topic so i need some help in understanding these percentile questions. Why is 1 percentile 15.5 in the case u mentioned ? Shouldn't it be 1/100*12 or 13. I am not sure why do 1 is added to the total number of items when percentile position is calculated? Is it to exclude the percentile position we are calculating i.e to calculate the percentage of values below say 1 percentile , but not including the value of 1 percentile? please explain.
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Re: The 500 students in a class took an examination. Sco [#permalink]
A:
You need to know that in a normal curve, the mean is exactly at the 50%ile, 1 standard deviation above the mean is 34%ile above that, and 2 standard deviations above the mean is 14%ile above that. In other words, 2 standard deviations above the mean is around 98%ile. Since Jamal is therefore at 98%ile and Charlie as at 5%ile, Charlie is closer to the mean and this answer is out.

Could someone explain this? Appreciate it!
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Re: The 500 students in a class took an examination. Sco [#permalink]
SherpaPrep wrote:
A:
You need to know that in a normal curve, the mean is exactly at the 50%ile, 1 standard deviation above the mean is 34%ile above that, and 2 standard deviations above the mean is 14%ile above that. In other words, 2 standard deviations above the mean is around 98%ile. Since Jamal is therefore at 98%ile and Charlie as at 5%ile, Charlie is closer to the mean and this answer is out.

B:
If Charlie is 5%ile, then he performed better than 5% of the total, or 25 people. Since Jamal is 98%ile, he performed better than 98% of the students, meaning about 2% of them, about 10 students, performed better than him. Since only about 35 people out of 500 performed either better or worse than them, 465 must have performed equal to Charlie or above or equal to Jamal or below, so we can see that this answer must be true.

C:
From the last answer choice, we know that we're looking at 465 people, which is well above 450, so this one is out.

D:
Since there are 500 students, every percentile must contain 5 students. The key to this one is the word "exactly". Since the 5th percentile falls between the 25th and 26th student, the 5th percentile itself is the average of the 25th and 26th students' scores. Since the scores are given in integers, if you average two of them, you'll either get an integer, or something that ends in a .5. But since Charlie couldn't have gotten a score that ends in a .5, this scenario is out.

What if the 25th lowest student had scored a 20 and the 26th lowest had gotten a 22? Then the 5th percentile would be 21, but since nobody actually got that score, this scenario is impossible.

The only way Charlie could've gotten exactly the 5th percentile is if the 25th and 26th lowest people got the same score, in which case the average of the two of them equals both of them. Thus, D is in.

Can you please explain why the 5th percentile score cannot be 21?
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Re: The 500 students in a class took an examination. Sco [#permalink]
Expert's post
If Jamal's score places him at approximately the 98_th percentile and Charlie's score was at the 5 percentile, then about 93% of the class scored between Jamal and Charlie since 93% of 500 is equal to 465.

I hope now is more clear to you why B is correct.

Regards
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Re: The 500 students in a class took an examination. Sco [#permalink]
Hi Carcass

Can you please share some theory on percentiles? I alway find these questions confusing. Hopefully some theory will help. Thanks
Founder  Joined: 18 Apr 2015
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Re: The 500 students in a class took an examination. Sco [#permalink]
Expert's post
Sue Use the gmatclub math book at page 16. Percentile is rather a simple concept. The questions as worded become tricky.

Attachment: GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]

feel free to ask further assistance

regards
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Re: The 500 students in a class took an examination. Sco [#permalink]
Hi Carcass

If Charlie out scored 25 students then his score must be the 26th score or the first in the 6th percentile. Why is 5th percentile the average of 25th and 26th score? Why it is not the 26th score below which 5% of the scores or 25 values lie? Some user above has calculated the position of the 5th percentile as 5/100 *501 =25.05. Why is 1 added to the total? GRE Instructor Joined: 10 Apr 2015
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Re: The 500 students in a class took an examination. Sco [#permalink]
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Expert's post
fifan wrote:
Hi Carcass

If Charlie out scored 25 students then his score must be the 26th score or the first in the 6th percentile. Why is 5th percentile the average of 25th and 26th score? Why it is not the 26th score below which 5% of the scores or 25 values lie? Some user above has calculated the position of the 5th percentile as 5/100 *501 =25.05. Why is 1 added to the total?

I'm not crazy about question D.
From what I've read in ETS's GRE literature, it's unclear how the GRE treats the calculation of percentiles when it comes down to the finer points.
For example, in the set of ages {1, 2, 3, 4, 5}, some will say that the age of 3 is a 40th percentile age (since 3 is greater than 40% of the ages), while others will insist that 2.5 (the average of 2 and 3) is a 40th percentile age.

So, for example, let's say the first 27 scores (out of 500 scores) are: 1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,6,6,7,7,7,7,8,9,10

The 26th score is 9
So,there are 25 scores less than 9
25/500 = 5%, so some would say that 9 is a 5th percentile score.
Others will say that 8.5 is the 5th percentile score.

I don't believe I've seen an official GRE question that hinges on the one concept.
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Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 27 Jan 2019
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Re: The 500 students in a class took an examination. Sco [#permalink]
Thanks Greenlight Prep

What is most that GRE can ask about percentiles?From your post i assume the GRE wont ask to calculate a particular percentile value from a set of given values since as u mentioned there is a difference of opinion. GRE Instructor Joined: 10 Apr 2015
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Re: The 500 students in a class took an examination. Sco [#permalink]
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Expert's post
fifan wrote:
Thanks Greenlight Prep

What is most that GRE can ask about percentiles?From your post i assume the GRE wont ask to calculate a particular percentile value from a set of given values since as u mentioned there is a difference of opinion.

I think the first 3 questions in this post are reasonable.
If there were a question that hinged on the exact calculation of percentiles, the test-makers would include some additional proviso (e.g., here's how to calculate 33rd percentile) to help you answer the question.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Re: The 500 students in a class took an examination. Sco   [#permalink] 09 Jul 2019, 05:43
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